Find a 4x4 magic square with magic constant being 188 (base ten) and each of whose 16 entries is a non leading zeroes positive binary palindrome.
*** Disregard rotations and reflections.
(In reply to
No Subject by Ady TZIDON)
If repetitions are allowed, as assumed in the first post, then of course any permutation of the 4 given numbers will work as assignments to the placeholders a, b, c and d, as will have any permutation of any one of these 139 sets:
1 1 21 165
1 1 33 153
1 1 93 93
1 3 31 153
1 3 65 119
1 3 85 99
1 5 17 165
1 5 63 119
1 7 15 165
1 7 27 153
1 7 51 129
1 7 73 107
1 9 51 127
1 9 85 93
1 15 45 127
1 15 65 107
1 15 73 99
1 17 17 153
1 17 51 119
1 17 63 107
1 17 85 85
1 21 73 93
1 27 31 129
1 27 33 127
1 31 63 93
1 51 51 85
1 51 63 73
3 3 17 165
3 3 63 119
3 5 15 165
3 5 27 153
3 5 51 129
3 5 73 107
3 7 51 127
3 7 85 93
3 15 17 153
3 15 51 119
3 15 63 107
3 15 85 85
3 21 45 119
3 21 65 99
3 27 31 127
3 27 51 107
3 27 65 93
3 27 73 85
3 33 33 119
3 33 45 107
5 5 51 127
5 5 85 93
5 9 9 165
5 9 21 153
5 9 45 129
5 15 15 153
5 17 73 93
5 21 33 129
5 21 63 99
5 27 27 129
5 27 63 93
5 31 33 119
5 31 45 107
5 33 51 99
5 33 65 85
5 45 45 93
5 45 65 73
7 7 9 165
7 7 21 153
7 7 45 129
7 9 45 127
7 9 65 107
7 9 73 99
7 15 73 93
7 17 45 119
7 17 65 99
7 21 31 129
7 21 33 127
7 27 27 127
7 31 31 119
7 31 51 99
7 31 65 85
7 33 63 85
7 45 51 85
7 45 63 73
7 51 65 65
9 9 17 153
9 9 51 119
9 9 63 107
9 9 85 85
9 15 45 119
9 15 65 99
9 17 33 129
9 17 63 99
9 21 31 127
9 21 51 107
9 21 65 93
9 21 73 85
9 27 33 119
9 27 45 107
9 31 63 85
9 33 73 73
9 51 63 65
15 15 31 127
15 15 51 107
15 15 65 93
15 15 73 85
15 17 27 129
15 17 63 93
15 21 33 119
15 21 45 107
15 27 27 119
15 27 73 73
15 33 33 107
15 45 63 65
17 17 27 127
17 21 21 129
17 21 31 119
17 21 51 99
17 21 65 85
17 27 45 99
17 27 51 93
17 31 33 107
17 33 45 93
17 33 65 73
17 45 63 63
21 21 27 119
21 21 73 73
21 27 33 107
21 31 51 85
21 31 63 73
21 51 51 65
27 27 27 107
27 31 31 99
27 31 45 85
27 31 65 65
27 33 63 65
27 45 51 65
31 31 33 93
31 31 63 63
31 33 51 73
33 45 45 65
Noteworthy is a set of all 27's with four scattered 107's.
DefDbl A-Z
Dim crlf$, bpal(100)
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
For i = 1 To 188
bi$ = base$(i, 2)
If isPal(bi) Then
bpPtr = bpPtr + 1
bpal(bpPtr) = i
End If
Next
Text1.Text = Text1.Text & bpPtr & crlf & crlf
For a = 1 To bpPtr
tot = bpal(a)
For b = a To bpPtr
tot = tot + bpal(b)
For c = b To bpPtr
tot = tot + bpal(c)
For d = c To bpPtr
DoEvents
tot = tot + bpal(d)
If tot = 188 Then
Text1.Text = Text1.Text & bpal(a) & " "
Text1.Text = Text1.Text & bpal(b) & " "
Text1.Text = Text1.Text & bpal(c) & " "
Text1.Text = Text1.Text & bpal(d) & " "
Text1.Text = Text1.Text & crlf
ct = ct + 1
End If
tot = tot - bpal(d)
Next
tot = tot - bpal(c)
Next
tot = tot - bpal(b)
Next
Next
Text1.Text = Text1.Text & crlf & ct & " done"
End Sub
Function base$(n, b)
v$ = ""
n2 = n
Do
d = n2 Mod b
n2 = n2 \ b
v$ = LTrim(Str(d)) + v$
Loop Until n2 = 0
base$ = v$
End Function
Function isPal(s$)
good = 1
For i = 1 To Len(s$) / 2
If Mid$(s$, i, 1) <> Mid$(s$, Len(s$) + 1 - i, 1) Then good = 0: Exit For
Next
isPal = good
End Function
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Posted by Charlie
on 2015-12-25 08:11:02 |
re: No Subject
